Artikel i vetenskaplig tidskrift, 2010

Let G be a step-two nilpotent group of H-type with Lie algebra G=V⊕t . We define a class of vector fields X={X j } on G depending on a real parameter k≥1 , and we consider the corresponding p -Laplacian operator L p,k u=div X (|∇ X u| p−2 ∇ X u) . For k=1 the vector fields X={X j } are the left invariant vector fields corresponding to an orthonormal basis of V ; for G being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator L p,k and as an application, we get a Hardy type inequality associated with X .